3-D Groundwater Contaminant Transport

In collaboration with Greg Whiffen and Christine Shoemaker of the Dept. of
Civil Engineering at Cornell University, we have applied ADIFOR to the TLS3D
3-D groundwater contaminant-transport code. TLS3D employs a
Taylor least squares finite-element procedure to solve the unsteady advection
diffusion equation.

We computed derivatives of the single-species contaminant concentrations at
each node at time step t + 1
to the flow field velocity vectors at time step t
on meshes
ranging in size from
4 to 32 rectangular box elements, corresponding to 48 to 432 independent
variables. We verified the derivatives computed by ADIFOR with central
differences. However, ADIFOR-generated derivatives can be computed much
faster. The table below shows the complexity of evaluation the model
(labelled f(x)) and the speedup that ADIFOR achieves over one-sided
divided differences.